being trained in chemistry one might expect that i could give you an answer. chemistry is after all an intense study of the properties of the very thing you pose your question about, namely matter. a chemist might be presented with a sample of some substance. he will want to know what type of matter it is. is it a mixture, a conglomerate an amalgm. a chemist will weigh the substance, subject it to magnetic fields, chemical tests, check its spectral properties, heat it, freeze it, try to disolve it or disolve something in it. boiling points, freezing points, crystaliztion propberties, diffusion rates might be checked. Electrical conductivity would be checked. the ph factor of the substance would be studied for acidity probperties. the list goes on and on. but any substance that you find and bring to a chemist would be a sample of matter. any sample of matter can be broken down into its constituent chemical molecules and atoms. atoms are more fundamentsl than molecules as molecules are made up of atoms. atoms may or may not be stable under some given condition such that they will either tend to form molecules with other atoms to become more stable or actually break down to become other types of atoms or isotopes of the same atom. any given type of atom has very specific elemental properties that are well recognized by chemists. if you break down a given atom into its constituents which are protons, electrons and neutrons and energy then you destroy the characteristics or properties that a given atom lends to the element that it makes up. things such as electronegativiy, density, refractive index, atomic weight, its reactivity, the physical state that it tends towards such as gaseousness, solid, liquid, metalic, nonmetalic or noble properties.
the electrons, neutrons and protons that make up matter have their own properties such as mass, size, charge and spin. fundamental particles such as electrons, neutrons and protons are still considered as being matter. there are more exotic material objects that are fundamental like electron, protons and neutrons that are also considered to be matter and are classified as elementary particles such as muons, pions, k-mesons ect. these particles all have antiparticles, mass, spin (even if it is zero), and life times. they all have quantum numbers L, B and S. the conservation laws of energy, momentum, angular momentum, charge and quantum number apply to these elementary particles.
did i forget to mention quarks? :)

hope this helps at least a little
regards tim